{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#本章需导入的模块\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['font.sans-serif']=['SimHei']  #解决中文显示乱码问题\n",
    "plt.rcParams['axes.unicode_minus']=False\n",
    "import warnings\n",
    "warnings.filterwarnings(action = 'ignore')\n",
    "from sklearn.metrics import confusion_matrix,f1_score,roc_curve, auc, precision_recall_curve,accuracy_score\n",
    "from sklearn.model_selection import train_test_split,KFold,LeaveOneOut,LeavePOut # 数据集划分方法\n",
    "from sklearn.model_selection import cross_val_score,cross_validate # 计算交叉验证下的测试误差\n",
    "from sklearn import preprocessing\n",
    "import sklearn.linear_model as LM\n",
    "from sklearn import neighbors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(123)\n",
    "N=200\n",
    "x=np.linspace(0.1,10, num=N)\n",
    "y=[]\n",
    "z=[]\n",
    "for i in range(N):\n",
    "    tmp=10*np.math.sin(4*x[i])+10*x[i]+20*np.math.log(x[i])+30*np.math.cos(x[i])\n",
    "    y.append(tmp)\n",
    "    tmp=y[i]+np.random.normal(0,3)\n",
    "    z.append(tmp)\n",
    "\n",
    "fig,axes=plt.subplots(nrows=1,ncols=3,figsize=(15,4))\n",
    "axes[0].scatter(x,z,s=5)\n",
    "axes[0].plot(x,y,'k-',label=\"真实关系\")\n",
    "\n",
    "modelLR=LM.LinearRegression()\n",
    "X=x.reshape(N,1)\n",
    "Y=np.array(z)\n",
    "modelLR.fit(X,Y)\n",
    "axes[0].plot(x,modelLR.predict(X),label=\"线性模型\")\n",
    "linestyle=['--','-.',':','-']\n",
    "for i in np.arange(1,5):\n",
    "    tmp=pow(x,(i+1)).reshape(N,1)\n",
    "    X=np.hstack((X,tmp))\n",
    "    modelLR.fit(X,Y)\n",
    "    axes[0].plot(x,modelLR.predict(X),linestyle=linestyle[i-1],label=str(i+1)+\"项式\")\n",
    "axes[0].legend()\n",
    "axes[0].set_title(\"真实关系和不同复杂度模型的拟合情况\")\n",
    "axes[0].set_xlabel(\"输入变量\")\n",
    "axes[0].set_ylabel(\"输出变量\")\n",
    "\n",
    "X=x.reshape(N,1)\n",
    "Y=np.array(z)\n",
    "modelLR.fit(X,Y)\n",
    "MSEtrain=[np.sum((Y-modelLR.predict(X))**2)/(N-2)]\n",
    "for i in np.arange(1,9):  \n",
    "    tmp=pow(x,(i+1)).reshape(N,1)\n",
    "    X=np.hstack((X,tmp))\n",
    "    modelLR.fit(X,Y)\n",
    "    MSEtrain.append(np.sum((Y-modelLR.predict(X))**2)/(N-(i+2)))\n",
    "axes[1].plot(np.arange(1,10),MSEtrain,marker='o',label='训练误差')\n",
    "axes[1].legend()\n",
    "axes[1].set_title(\"不同复杂度模型的训练误差\")\n",
    "axes[1].set_xlabel(\"模型复杂度\")\n",
    "axes[1].set_ylabel(\"MSE\")    \n",
    "\n",
    "X=x.reshape(N,1)\n",
    "Y=np.array(z)\n",
    "for i in np.arange(1,5):  #采用5项式模型\n",
    "    tmp=pow(x,(i+1)).reshape(N,1)\n",
    "    X=np.hstack((X,tmp))    \n",
    "np.random.seed(0)\n",
    "size=np.linspace(0.2,0.99,100)\n",
    "MSEtrain=[]\n",
    "for i in range(len(size)):\n",
    "    Ntraining=int(N*size[i])\n",
    "    id=np.random.choice(N,Ntraining,replace=False)\n",
    "    X_train=X[id]\n",
    "    y_train=Y[id]\n",
    "    modelLR.fit(X_train,y_train)\n",
    "    MSEtrain.append(np.sum((y_train-modelLR.predict(X_train))**2)/(Ntraining-6))    \n",
    "\n",
    "tmpx=np.linspace(1,len(size), num=len(size)).reshape(len(size),1)  #拟合MSE\n",
    "tmpX=np.hstack((tmpx,tmpx**2))\n",
    "tmpX=np.hstack((tmpX,tmpx**3))\n",
    "modelLR.fit(tmpX,MSEtrain)\n",
    "\n",
    "axes[2].plot(size,MSEtrain,linewidth=1.5,linestyle='-',label='MSE')\n",
    "axes[2].plot(size,modelLR.predict(tmpX),linewidth=1.5,linestyle='--',label='MSE趋势线')\n",
    "axes[2].set_title(\"训练样本量和训练MSE\")\n",
    "axes[2].set_xlabel(\"训练样本量水平\")\n",
    "axes[2].set_ylabel(\"MSE\")\n",
    "axes[2].legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "说明：\n",
    "1、这里通过数据模拟直观展示模型复杂度和训练误差的关系。随模型复杂度的提高，训练误差单调下降。\n",
    "2、首先设定输入变量和输出变量的真实关系，并通过加上服从正态分布的随机数模拟其他随机因素对输出变量的影响。这里，设定的真实关系函数可以被泰勒展开，因此一定是次数越高的多项式模型越贴近真实观测值。 到达一定阶数（这里为9）后继续增加阶数对参数估计结果的影响很小可以忽略，无需再增加阶数。\n",
    "3、分别建立各个多项式模型。这里消除了模型复杂度本身导致对MSE计算结果的影响，MSE计算时分母为自由度：样本量-(输入变量个数+1)。\n",
    "4、考察训练集样本量对对于特定模型（这里为五项式）学习充分性的影响。样本量依次为原数据集的20%至99%。这里消除了样本量本身对MSE计算结果的影响，MSE计算时分母为自由度：样本量-(输入变量个数+1)。对不同样本量下的MSE进行三次曲线拟合。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axes=plt.subplots(nrows=1,ncols=2,figsize=(10,4))  \n",
    "modelLR=LM.LinearRegression()\n",
    "\n",
    "np.random.seed(123)\n",
    "Ntraining=int(N*0.7)\n",
    "Ntest=int(N*0.3)\n",
    "id=np.random.choice(N,Ntraining,replace=False)\n",
    "X_train=x[id].reshape(Ntraining,1)\n",
    "y_train=np.array(z)[id].reshape(Ntraining,1)\n",
    "modelLR.fit(X_train,y_train)\n",
    "MSEtrain=[np.sum((y_train-modelLR.predict(X_train))**2)/(Ntraining-2)]\n",
    "\n",
    "xtest= np.delete(x, id).reshape(Ntest,1)\n",
    "X_test= np.delete(x, id).reshape(Ntest,1)\n",
    "y_test=np.delete(z,id).reshape(Ntest,1)\n",
    "MSEtest=[np.sum((y_test-modelLR.predict(X_test))**2)/(Ntest-2)]\n",
    "\n",
    "for i in np.arange(1,9):\n",
    "    tmp=pow(x[id],(i+1)).reshape(Ntraining,1)\n",
    "    X_train=np.hstack((X_train,tmp))\n",
    "    modelLR.fit(X_train,y_train)\n",
    "    MSEtrain.append(np.sum((y_train-modelLR.predict(X_train))**2)/(Ntraining-(i+2)))\n",
    "    tmp=pow(xtest,(i+1)).reshape(Ntest,1)    \n",
    "    X_test=np.hstack((X_test,tmp))\n",
    "    MSEtest.append(np.sum((y_test-modelLR.predict(X_test))**2)/(Ntest-(i+2)))\n",
    "\n",
    "axes[0].plot(np.arange(1,10,1),MSEtrain,marker='o',label='训练误差')\n",
    "axes[0].plot(np.arange(1,10,1),MSEtest,marker='*',label='测试误差')\n",
    "axes[0].legend()\n",
    "axes[0].set_title(\"不同复杂度模型的训练误差和测试误差\")\n",
    "axes[0].set_xlabel(\"模型复杂度\")\n",
    "axes[0].set_ylabel(\"MSE\")\n",
    "\n",
    "MSEtrain=[]\n",
    "MSEtest=[]\n",
    "for j in range(20):\n",
    "    x=np.linspace(0.1,10, num=N)\n",
    "    id=np.random.choice(N,Ntraining,replace=False)\n",
    "    X_train=x[id].reshape(Ntraining,1)\n",
    "    y_train=np.array(z)[id].reshape(Ntraining,1)\n",
    "    modelLR.fit(X_train,y_train)\n",
    "    mse_train=[np.sum((y_train-modelLR.predict(X_train))**2)/(Ntraining-2)]\n",
    "\n",
    "    xtest= np.delete(x, id).reshape(Ntest,1)\n",
    "    X_test= np.delete(x, id).reshape(Ntest,1)\n",
    "    y_test=np.delete(z,id).reshape(Ntest,1)\n",
    "    mse_test=[np.sum((y_test-modelLR.predict(X_test))**2)/(Ntest-2)]\n",
    "\n",
    "    for i in np.arange(1,9):\n",
    "        tmp=pow(x[id],(i+1)).reshape(Ntraining,1)\n",
    "        X_train=np.hstack((X_train,tmp))\n",
    "        modelLR.fit(X_train,y_train)\n",
    "        mse_train.append(np.sum((y_train-modelLR.predict(X_train))**2)/(Ntraining-(i+2)))\n",
    "        tmp=pow(xtest,(i+1)).reshape(Ntest,1)    \n",
    "        X_test=np.hstack((X_test,tmp))\n",
    "        mse_test.append(np.sum((y_test-modelLR.predict(X_test))**2)/(Ntest-(i+2)))\n",
    "    plt.plot(np.arange(1,10),mse_train,marker='o',linewidth=0.8,c='lightcoral',linestyle='-')\n",
    "    plt.plot(np.arange(1,10),mse_test,marker='*',linewidth=0.8,c='lightsteelblue',linestyle='-.')\n",
    "    MSEtrain.append(mse_train)\n",
    "    MSEtest.append(mse_test)\n",
    "    \n",
    "MSETrain=pd.DataFrame(MSEtrain)\n",
    "MSETest=pd.DataFrame(MSEtest)\n",
    "axes[1].plot(np.arange(1,10),MSETrain.mean(),marker='o',linewidth=1.5,c='red',linestyle='-',label=\"训练误差的期望\")\n",
    "axes[1].plot(np.arange(1,10),MSETest.mean(),marker='*',linewidth=1.5,c='blue',linestyle='-',label=\"测试误差的期望\")\n",
    "axes[1].set_title(\"不同复杂度模型的训练误差和测试误差及其期望\")\n",
    "axes[1].set_xlabel(\"模型复杂度\")\n",
    "axes[1].set_ylabel(\"MSE\")\n",
    "axes[1].legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "说明：\n",
    "1、这里通过数据模拟直观展示不同复杂度模型下训练误差和测试误差的关系。随模型复杂度的提高，训练误差单调下降，测试误差呈先下降后来上升的U字形。\n",
    "2、从数据集中随机抽取一定比例的样本观测组成训练集训练模型，剩余的样本观测组成测试集计算测试误差。这里进行了20次。\n",
    "3、样本观测的随机抽取必然导致20个训练集包含可能不同的样本观测，由此模型的参数估计值会有差别，从而使得20个训练误差和测试误差的数值结果不尽相等。带圆点的浅红色和浅灰色分别对应20次抽样的训练误差和测试误差，它们各自的均值对应带星号的红色和蓝色线。\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
